It sounds like this would be a case for a paired-samples t test (or a Wilcoxon signed-rank test if you choose a non-parametric test).

By the way, variables cannot be "non-parametric;" only statistical tests can be. You would potentially use a non-parametric test if your variables are ranks, ordinal-scale, or if the difference score variable [post - pre] is not normally distributed.

According to your description:

Since you have two related continuous measurements for each subject (before and after), and your data do not meet the assumptions required for parametric tests, the appropriate non-parametric test to use is the Wilcoxon signed-rank test. This test compares the median of the differences to zero and determines whether the speeds after the letter are consistently lower than those before.

On SPSS > Analyze → Nonparametric Tests → Legacy Dialogs → 2 Related Samples

Then >

- Move Column[Speed Before] into Test Variable1 and Column[Speed After] into Test Variable2.

- Under Test Type, tick Wilcoxon (uncheck Sign if you want the more powerful rank version).

-> Click OK.

Then > look at the Asymp. Sig. (2-tailed) column:

If p ≤ .05, you conclude a significant change in speeds.

Ranks table also shows how many increased vs. decreased.

By the way, if you're concerned about wildly skewed differences or want an even more straightforward approach that only considers direction (not magnitude), you can choose the Sign test in the same dialog. It's less powerful but makes almost no distributional assumptions.

Sophie Lee

SPSS does effectively remove ties from the Wilcoxon rank sums. That's by design, not a bug.

In the Wilcoxon signed-rank test SPSS runs, "Ties" are precisely those paired differences that equal zero (i.e., Speed_After – Speed_Before = 0). Because the test is based on ranking the magnitude of non-zero differences (and then looking at their sign), any zero‐difference pair -> cannot be assigned a positive or negative rank, -> is therefore omitted from the rank sum calculations, and shows up in your output under the "Ties" count.

They're not "deleted" from your dataset, they simply do not contribute to W+ or W- => Your effective N for the Wilcoxon test is N(used) = N(total pairs) - N(ties)

=Someone might ask, Why do ties get dropped?

Simply because a tied pair provides no information about direction (increase vs. decrease), so it can't inform the signed-rank statistic. However, if you have a lot of ties -> your test loses power (fewer data points contributing).

=In that case, what can you do?

>Check how many ties you have.

-If it's only a handful -> you can safely proceed.

-If you have many ties ->

#Consider the Sign test (also omits ties but is even simpler—only looks at direction, not magnitude). It will still list the number of ties, but because it only compares counts of "+" vs "–", it's less sensitive to the magnitude of differences and sometimes preferable if your data are very "steppy". [ I mean lots of identical or rounded difference values (few unique values), resulting in many ties under Wilcoxon's ranking scheme—so the data look like a series of "steps" rather than a smooth continuum. Concretely: If many drivers' speed changes cluster at, say, exactly 0 km/h, ±1 km/h, or ±2 km/h—and very few at other values—that creates large blocks of tied ranks in the Wilcoxon test. Those tied blocks mean most of your data don't contribute meaningful rank‐sum information, which weakens the test's power In contrast, the Sign test only cares about whether each difference is positive, negative, or zero—so a handful of small discrete jumps ("steps") still count directionally and you lose less information.]

#Report both tests to see if they agree, + Report your actual N in your write-up. "Of the 50 paired observations, 5 were ties (no change) and omitted; Wilcoxon N= 45, Z=.. P=.."

#Inspect the zero-difference cases to see if there's anything systematic (e.g., a rounding issue, or truly no change for a subgroup).

Hi,

Normalize the data first, then use a Paired t-test, as both variables are scales, and data is captured against two intervals before and after.